Our measurements of high-resolution spectra of Mars at 3.7 and 8 mu m revealed 200 lines of (OCO)-O-16-C-12-O-17, (OCO)-O-16-C-12-O-18, and (OCO)-O-16-C-13-O-18 isotopes. Among them are 38 lines which are absent in spectroscopic databases, Eighty lines of the three isotopes with closely equivalent widths were chosen to determine the oxygen and carbon isotope ratios in CO2. A radiation transfer code which coupled the reflected solar and thermal radiation was developed, This code divided the atmosphere into 30 layers and the Voigt profile of each line in each layer into 60 intervals. This results in a determination of the atmospheric pressure P-0 = 7.4 +/- 0.4 mbar and the isotope ratios O-18/O-17 = 0.914 +/- 0.04 and C-13/C-12 = 0.94 +/- 0.15 scaled to CO2 in the Earth's atmosphere. Scaling to SMOW gives O-18/O-17 = 0.93 +/- 0.04; assuming the same initial isotope ratio on Mars and Earth, we find that O-18/O-16 = 0.87 +/- 0.08 in CO2 on Mars. Oxygen and carbon isotope fractionation factors of 0.774 and 0.891 in the escape processes were calculated using individual heights of homopauses for different species. Oxygen and carbon isotope ratios are determined by the present water amount, the regolith-atmosphere-cap reservoir of CO2, the carbonate abundance, the initial abundance of CO2, and losses of H2O and CO2 by escape processes. Two processes affect the carbon isotope ratio in the atmosphere: formation of carbonates and sputtering of CO2. This ratio was calculated as a function of the CO2 sputtering after the end of impact erosion of the atmosphere at 0.8 byr. A weighted-mean value of C-13/C-12 = 0.97 +/- 0.05 (scaled to PDB) for three measurements in the martian atmosphere and determinations of the carbon isotope ratio in carbonates of the SNC meteorites require CO2 escape by sputtering to be smaller than 10 mbar. The oxygen isotope ratio could be depleted in water early in the history of Mars by water-silicate equilibrium; this does not contradict the isotopic composition of the SNC meteorites, Fractionation with CO2 and loss of CO2 by impact erosion depleted heavy oxygen in water as well. We calculated delta(18)O approximate to -70 parts per thousand in water vapor for preferred values of the initial CO2 of 7.5 bars, water escape of 30 m, and the present water ice reservoir of 500 m, Taking into account uncertainities of these values by a factor of 2-3, the expected minimum value of delta(18)O in water vapor is close to -110 parts per thousand and does not agree with some recent determinations. Heavy oxygen in CO2 should either be equal to that in water vapor (in the case of photochemical mixing) or exceed that in water vapor by 90 parts per thousand (in the case of thermodynamic equilibrium). Currently the calculated values of delta(18)O may serve as a guide to measured values which show large scatter and uncertainties. (C) 1996 Academic Press, Inc.